IRREDUNDANCE PERFECT GRAPHS

The domination number gamma(G) and the irredundance number ir(G) of a graph G have been considered by many authors. It is well known that ir(G) less than or equal to gamma(G) holds for all graphs G. In this paper we investigate the concept of irredundance perfect graphs which deals with those graphs that have all their induced subgraphs H satisfying ir(H) = gamma(H). We give a characterization of those graphs G for which ir(H)= gamma(H) for every induced subgraph H of G with ir(H)= 2 in terms of 30 forbidden induced subgraphs. A sufficient condition for ir(G) = gamma(G) for a graph G with ir(G) less than or equal to 4 is given in terms of three forbidden subgraphs. This result strengthens a conjecture due to Favaron (1986) which states that if a graph G does not contain these three forbidden subgraphs, then ir(G) = gamma(G).